00:00:00 / 00:00:00

Reconciling the Gaussian and Whittle Likelihood with an application to estimation in the frequency domain

By Suhasini Subba Rao

Appears in collection : New Results on Time Series and their Statistical Applications / Séries chronologiques: nouveaux résultats et applications statistiques

In time series analysis there is an apparent dichotomy between time and frequency domain methods. The aim of this paper is to draw connections between frequency and time domain methods. Our focus will be on reconciling the Gaussia likelihood and the Whittle likelihood. We derive an exact, interpretable, bound between the Gaussian and Whittle likelihood of a second order stationary time series. The derivation is based on obtaining the transformation which is biorthogonal to the discrete Fourier transform of the time series. Such a transformation yields a new decomposition for the inverse of a Toeplitz matrix and enables the representation of the Gaussian likelihood within the frequency domain. We show that the difference between the Gaussian and Whittle likelihood is due to the omission of the best linear predictions outside the domain of observation in the periodogram associated with the Whittle likelihood. Based on this result, we obtain an approximation for the difference between the Gaussian and Whittle likelihoods in terms of the best fitting, finite order autoregressive parameters. These approximations are used to define two new frequency domain quasi-likelihoods criteria. We show these new criteria yield a better approximation of the spectral divergence criterion, as compared to both the Gaussian and Whittle likelihoods. In simulations, we show that the proposed estimators have satisfactory finite sample properties.

Information about the video

Citation data

  • DOI 10.24350/CIRM.V.19655003
  • Cite this video Subba Rao, Suhasini (17/09/2020). Reconciling the Gaussian and Whittle Likelihood with an application to estimation in the frequency domain. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19655003
  • URL https://dx.doi.org/10.24350/CIRM.V.19655003

Bibliography

  • RAO, Suhasini Subba et YANG, Junho. Reconciling the Gaussian and Whittle Likelihood with an application to estimation in the frequency domain. arXiv preprint arXiv:2001.06966, 2020. - https://arxiv.org/abs/2001.06966

Last related questions on MathOverflow

You have to connect your Carmin.tv account with mathoverflow to add question

Ask a question on MathOverflow




Register

  • Bookmark videos
  • Add videos to see later &
    keep your browsing history
  • Comment with the scientific
    community
  • Get notification updates
    for your favorite subjects
Give feedback
Loading…
Loading the web debug toolbar…
Attempt #